Question

Find the measure of angle x in the figure below: Two triangles are shown such that one triangle is inverted and they share a common vertex. The lower triangle has two angles at the base. The lower left angle is marked as 45 degrees. The lower right angle is marked as 55 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees. The angle at the vertex of the bottom triangle is marked as y degrees. 45° 80° 55° 100°

Answer 1

Y can be found by setting the 3 angles in the bottom triangle equal to 180 degrees like so:

45 + 55 + y = 180

100 + y = 180 (Simplify)

y = 80 (Subtract 100 from both sides)

Angles x and y are opposite angles, so they are equal to each other. This means that x = 80 degrees also.